# Calculation of rafters and trusses for hip and gable roofs

The rafters are calculated after selecting the layout scheme, mutually attaching the legs in the skate, and the method of joining to the power plate. This will allow the first stage to determine the direction of the efforts transmitted by the bar / board to the walls. Independent calculations are complex, require practice, knowledge of geometry, physics. For the convenience of developers who have decided to save on the manufacture of the project truss system, on the Internet there are free services for approximate calculations.

The device truss system.

## Non-contoured suspended rafters

Builders use several options for fixing the slant rafters:

• cutting in the power plate with gouging or mounting in the supporting bar, horizontal bevel cutting in skate;
• slider in the lower part; bolted joint in the ridge with emphasis into the girder;
• lower slider in combination with rigid fastening of the upper part.

Figure 1. Scheme of gussets.

In all the above schemes, the design of the hanging trusses takes into account the minimum deflection of the rafter, the maximum bend in the skate support. Suspended rafters are the most reliable. Even if hanging rafters are not calculated, the safety margin is provided by the design itself.

In all variants, one hinge ensures the rotation of the rafter legs, the second - rotation of the trusses with the possibility of slippage in the support. The industry produces special slide assemblies that facilitate mounting at height. For the calculation using the ideal scheme - the same snow load, wind load falls on the roof (Fig. 1).

In practice, snow lingers unevenly on the slope planes. However, the static stability of the gable roof system will be maintained in each specified case, if the main condition is met - a rigid fixation in the ridge to the girder. The absence of horizontal displacement in the ridge run is ensured in several ways:

• both sides of the timber are attached to the gable roof gables;
• slanty rafters are made on the roof.

Calculation scheme rafters.

The tweezer roof cannot be supported on gables, therefore it is possible to shift towards the slope with a smaller load. Therefore, a horizontal scramble is used that performs an emergency function - it will not allow the roof to fall down at the maximum displacement of the ridge purlin. This element is mounted at a height of 1.7-2 m, observing two conditions:

• as low as possible to the power plate;
• there are no obstacles when walking around the attic.

Before calculating the rafters, it is necessary to determine the presence of a ridge girder in the system. This element is achieved by the absence of horizontal displacement of the upper conjugation of the roof slopes. Therefore, if the racks for the run interfere with operation (a variant of the attic room), then the rafters need to be calculated for static stability.

## Independent calculation of the truss system

Calculations for the hip roof, gable structures with gables are the simplest. The stability in these schemes is provided constructively; during the installation of contractions, the emergency response strength margin ensures the maximum operational period.

The simplest calculation of a rafter with a cut in a mauerlat, vertically trimmed in a skate (Fig. 2) looks as follows:

Figure 2. Simplest calculation rafters with a cut-in mauerlat, vertical trimming in the ridge.

• loads are calculated - special include hurricane winds, variables - wind pressure, amount of snow cover in the region of operation, constant - weight of roofing pie, truss system;
• determines the length of the truss legs - for this you need to decide on the materials of the roof, floors;
• the step of the rafters is calculated, it is necessary to take into account the type of roof, the presence of pipes, chimneys;
• the cross section of the beam is calculated - instead used board or log.

In practice, the calculation of the rafters is made according to the tables of SNiP for structural, roofing materials, loads by regions of the country.

The weight of the roofing pie of a gable, hip, gable, hip roof is folded in layers. From the tables, data for the weight of a square meter of materials is taken, the figures are added, the sum is multiplied by the safety factor 1.1. For example, for an ondulin with insulation, waterproofing, periodic crate from an inch board, the weight of the roof will be:

15 kg (board) + 10 kg (basalt wool) + 5 kg (waterproofing) + 3 kg (ondulin) = 33 kg x 1.1 = 34.1 km 2.

Experts recommend for light roofing materials to take a load with a margin of 50 kg per unit area. Since the own weight of the timber at this stage is still unknown, the section is selected later. Taking into account the correction factor, the load will be 55 kg, and this is used in further calculations.

Formulas for calculating the cubic capacity of a beam on the roof system of the house.

Roof rafters in different regions withstand varying wind, snow loads. Calculation of rafters in the snow is made according to the formula:

N 1 = S * k, where k is the coefficient of slope dependence, S is the mass of snow per square plot in the region of operation.

Both values ​​are present in the SNiP tables. For example, for a gradient of 25-60˚, the coefficient is 0.7; 10-25˚ angles is 1. For the Moscow region, the snow cover weight is 180 kg. Therefore, for 30-degree slopes, the load will be 180 * 0.7 = 126 kg.

Wind load is calculated in the same way:

N 2 = W * k, where k is the coefficient depending on the height of the cottage, region of operation, W is the wind norm of the terrain.

In addition, the type of terrain in the building spot is taken into account, therefore, for open spaces, coasts, the coefficient is always higher than for a forest, dense development:

• height 2-5 m - 0 , 75 or 0.85 units. ;
• The height of 5.1-10 m - 0.65 or 1 unit. ;
• height 10.1–20 m - 0.85 or 1.25 units.

The table of coefficients for calculating the elements of the truss system.

Thus, for a Moscow chalet with a height of 5 m and a wind load of 23 kg / m 2 we get:

23 * 0.75 = 17.25 kg .

The length of truss legs is determined depending on the slope of the slopes, the location of the ridge. It is calculated by the Pythagorean theorem, in which is the hypotenuse of the triangle. After determining this value from the table, the recommended lumber cross-section is taken, which will withstand all loads with allowable deflection (usually 1/200 of the length).

The table below contains the dependencies of the sawn timber section of truss legs on the span length of the trusses:

 L span (cm) Section (height / thickness, cm) bar board 500 20x10 22x8 400 15x10 20x6 or 18x8 300 12x10 15x8 or 16x5

The sections of truss drawbars are selected in the same way:

 Span (m) Section of the material (cm) 6 22x12 5 20x12 4 18x10 3 15x10 2 12x8

It remains to post s roof trusses so that they withstand all loads that normally distributed them, passed on through the load-bearing walls mauerlat. That is, the rafter step is calculated, which is then adjusted according to the value obtained. To do this, use the table again, which indicates the recommended distance between trusses (Fig. 3).

Figure 3. Table of rafters distances.

The length of the ridge is divided by the step of the rafter legs, a unit is added, the number of roof trusses is obtained. The value is rounded up, and the exact distance between the centers is calculated. When mounting, first install side triangles, then intermediate ones. Near chimneys, wooden structures are displaced by 30 cm, in accordance with fire safety requirements.

During the operation of the roof, periodic walking on it is assumed. This condition is especially relevant for slopes within 45 °, since it is necessary to throw off snow from them. Therefore, the weight of a person (100-150 kg) is added to the existing loads, providing an additional strength margin.

## Quality of sawn timber truss system

Gantry roof rafters are more often calculated for wooden structures. Therefore, the quality of lumber significantly affects the life of the power frame. The best option is a timber or elements assembled from boards. Wood of natural moisture gives greater shrinkage, which must be taken into account when rigid fixation of the rafters.

Sliding fasteners provide sufficient mobility of individual elements, but can only be used in certain schemes.

Figure 4. Calculation of rafters on the hipped roof.

For hip roof, sawn timber is recommended with the following parameters:

• 3 knots per meter of length;
• size of knots within 3 cm;
• no through cracks.

By installing the roof from the board, the chamber drying beam, the developer reduces shrinkage and increases the life of the structure. Processing fire retardants, antiseptics is mandatory, in the operated attic rooms, you must use a vapor barrier membrane, mounted under the cladding walls. Calculation of rafters on a hip roof does not differ from the standard, used for hip, gable configuration (Fig. 4).

## Spacing rafters of a hull-type

The same methods are used for the calculation of a roof using rafted rafters as for hanging ones.The differences are in the way of fixing the legs to the mauerlat, in the skate. In this case, you must have two supports, the material is bending, the design completely transfers the load to the main walls.

Calculations for crushing of the material can be added to the roof calculations, if necessary, while supporting the upper ends of the legs through the ridge girder. In the case of naps, the rafters compensate for spacer loads of each other. The contractions in these schemes work in compression, these details relieve the excessive tension that squeezes the walls around the perimeter.

The home wizard will not be able to calculate the rafters on the roof in professional programs, since working in graphic editors requires special training and practice. Online resources will help to avoid serious mistakes, just pick up the cross-section of the timber from which the roof truss is assembled, step, length. Timber is traditionally chosen with a margin, factory-made fasteners greatly facilitate self-construction.